Analysis of an M/M/1 driven fluid queue with multiple exponential vacations

The main purpose of the current paper is to study a fluid queue model driven by an M/M/1 queue with multiple exponential vacations. We drive an explicit expression for the stationary distribution of the buffer content in terms of modified Bessel function of first kind by employing generating function methodology. Several concrete examples are considered to illustrate the variation of the proposed model with respect to vacations.